You really shouldn't play Dudley heavily based around machine-gun combos or air-juggles. Just really unreliable. Playing a mix-up ground game with your Target combos and etc are a much better way to do it IMO. That's not to say a good machine-gun combo isn't too shabby every once and awhile.
MP -> Corkscrew,
c.MP -> Corkscrew,
HK -> Corkscrew,
Rocket Upper -> Corkscew,
hcb+k -> Corkscrew
c.MP -> Rocket Upper -> Corkscrew
These are the main ones I use for it normally for SA3
Oh and for quick reference, c.hk -> LP Machine-Gun, f.HP is roughly the same damage as c.hk -> hcf+lk, k